Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 349830.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
349830.o1 | 349830o4 | \([1, -1, 0, -16188795, -25011558675]\) | \(133345896593725369/340006815000\) | \(1196396858978731215000\) | \([2]\) | \(29491200\) | \(2.9209\) | |
349830.o2 | 349830o2 | \([1, -1, 0, -1404675, -58920939]\) | \(87109155423289/49979073600\) | \(175863553410559809600\) | \([2, 2]\) | \(14745600\) | \(2.5743\) | |
349830.o3 | 349830o1 | \([1, -1, 0, -917955, 337366485]\) | \(24310870577209/114462720\) | \(402764981867089920\) | \([2]\) | \(7372800\) | \(2.2278\) | \(\Gamma_0(N)\)-optimal |
349830.o4 | 349830o3 | \([1, -1, 0, 5591925, -474518979]\) | \(5495662324535111/3207841648920\) | \(-11287572788413202388120\) | \([2]\) | \(29491200\) | \(2.9209\) |
Rank
sage: E.rank()
The elliptic curves in class 349830.o have rank \(0\).
Complex multiplication
The elliptic curves in class 349830.o do not have complex multiplication.Modular form 349830.2.a.o
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.